Satellite-based global positioning systems are well known. For example, U.S. Pat. No. 5,210,540 (the "'540 patent"), issued to Masumota discloses a global positioning system for locating a mobile object, such as an automobile, in a global geometrical region. As described therein, the system includes a Global Positioning System (GPS) receiver for receiving radio waves from a plurality of satellites and outputting either two or three dimensional position data indicative of the present position of the mobile object. For greater accuracy, an altimeter is also employed to detect the mobile object's relative altitude. U.S. Pat. No. 5,430,654 (the "'654 patent"), issued to Kyrtsos et al discloses apparatus and methods for determining the position of a vehicle at, or near the surface of the earth using a satellite-based navigation system, wherein "precise" position estimates are achieved by reducing the effective receiver noise. The respective '540 and '654 patents are incorporated herein by reference for all they disclose and teach.
In particular, the Global Positioning System is a satellite-based navigation system that was designed and paid for by the U.S. Department of Defense. The GPS consists of twenty-four satellites, which orbit the earth at known coordinates. The particulars of the GPS are described in section 3.4.2 of "Vehicle Location and Navigation Systems," by Yilin Zhao, Artech House, Inc., 1997, which is fully incorporated herein by reference. As noted therein, the observation of at least four GPS satellites simultaneously will permit determination of three-dimensional coordinates of a receiver located on the earth's surface, as well as the time offset between the receiver and the respective satellites.
One problem encountered in global positioning systems is ionicspheric interference. The ionosphere is a dispersive medium, which lies between seventy and one thousand kilometers above the earth's surface. The ionosphere effects a certain, frequency dependent propagation delay on signals transmitted from the respective GPS satellites. The ionosphere also effects GPS signal tracking by the receiver. Notably, the ionospheric delay of a transmitted GPS signal can cause an error of up to ten meters when calculating the exact geographic position on the earth's surface of the receiver.
As demonstrated below, delay from ionospheric interference can be almost completely corrected for by using multiple frequency observations, i.e., by transmitting and receiving signals at two different, known GPS frequencies, L.sub.1 and L.sub.2, from a respective satellite. However, for security reasons, most GPS receivers do not receive the L.sub.2 frequency. Instead, these single (i.e., L.sub.1) frequency receivers can employ a model to estimate and correct for transmission delay due to ionospheric interference.
For example, the Global Positioning System, Interface Control Document, ICD-GPS-200, Revision C, Initial Release, Oct. 10, 1993, provides a method for ionospheric correction based on an "approximate atmospheric" model, which is dependent on a "total electron content" (TEC) model. In accordance with this model, and using only the L.sub.1 signal transmission frequency, it can be shown that the error .DELTA.S.sub.1 in the true satellite to receiver/user distance .rho. is ##EQU1## where F.sub.pp, is an "obliquity factor": ##EQU2## where R.sub.e is the radius of the earth, H.sub.r is the height of the maximum electron density in the ionosphere from the earth's surface, and .phi. is the angle between the respective satellite and a plane tangent to the earth's surface at the receiver's position.
Notably, the true TEC value of the ionosphere is very difficult to model and is highly sensitive to variables, such as time of day, solar activity and relative incident angle of the satellite with respect to the sunlight trajectory (if any) toward the receiver location, etc. In particular, the TEC nominal value varies widely, within a range of between 10.sup.16 to 10.sup.19. As a result, the above ionospheric correction model has been shown to adequately correct for no more than 50% of the ionospheric transmission delay.
As noted above, a dual frequency receiver can virtually eliminate ionospheric errors by computing the pseudo-range distance of the respective satellite on both the L.sub.1 and L.sub.2 frequencies. For purposes of illustration, a short derivation of such a dual frequency correction methodology is as follows:
Let .DELTA.S.sub.1 and .DELTA.S.sub.2 represent the error in the pseudo-range distances computed at frequencies L.sub.1 and L.sub.2, respectively. Then: ##EQU3## where .lambda..sub.L1 and .lambda..sub.L2 are the respective pseudo-range distances computed at frequencies L.sub.1 and L.sub.2, respectively, and .rho. is the true satellite to receiver distance. Dividing equation (3) by equation (4), results in: ##EQU4## Subtracting equation (4) from equation (3), gives: EQU .DELTA.S.sub.1 -.DELTA.S.sub.2 =.lambda..sub.L1 -.lambda..sub.L2(6)
Substituting equation (5) into equation (6), and after some minor algebraic manipulation, provides: ##EQU5##
Importantly, all quantities in the above expression (7) are either known by the receiver, or can be measured, with the TEC value totally canceled out of the equation.
Of course, in a GPS-based locating system having only a single (i.e., L.sub.1) frequency receiver, the above-described ionospheric correction model based on both the L.sub.1 and L.sub.2 transmission frequencies can not be employed.